Question

Let f: R → R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(x)f(y) for all x, y ∈ R. Then, then value of loge (f(4)) is .....

Answer 1

We have

f(x + y) = f(x)f'(y) + f'(x)f(y)

and f(0) = 1